Transient Phenomena in Quantum Bound States Subjected to a Sudden Perturbation

Abstract

Transient phenomena in quantum mechanics have been of interest to one of the authors (MM) for a long ago and, and in this paper, we focus on the problem of a potential V₋ which, for negative times, gives rise to bound states and is suddenly changed at t = 0 to a potential V₊ which includes V₋ plus a perturbed term. An example will be the deuteron (where the proton and neutron are assumed to interact through an oscillator potential) submitted to a sudden electrostatic field. The analysis for t > 0 can be carried out with the help of appropriate Feynman propagators, and we arrive at the result that the separation between the nucleons has an amplitude that depends on the intensity of the electrostatic field, but its period continues to be related to the inverse of the frequency of the oscillator proposed for the interaction. A general approximate procedure for arbitrary problems of this type is also presented at the end.